Abstract
Due to their strong image description ability, in recent years, quaternion exponential moments (QEMs) have attracted wide attention from relevant researchers. However, there is a numerical instability problem with QEMs because they can only take integer orders, and this problem restricts the performance of QEMs in image reconstruction and noise resistance. In this paper, the concept of fractional order is introduced and incorporated into exponential moments (EMs) and fractional-order exponential moments (FrEMs) are proposed; then the FrEMs are extended to fractional-order quaternion exponential moments (FrQEMs) that are suitable for color images and have better performance than QEMs in noise resistance and image reconstruction; subsequently, it is proved that FrQEMs are invariant to rotation; and finally, the properties of FrQEMs are experimentally analyzed and FrQEMs are used for object recognition. The experimental results show that FrQEMs have very excellent performance in color image reconstruction, high noise resistance, good rotation invariance and object recognition in color images.
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